Plot area with equation

Hello everyone,

I want to plot an area on a sphere, which is defined with the following equations:

R = 50

could somebody help?

Best regards

Alex

Answer 1

[Abdolkarim Mohammadi]

r = 50;
NumPoints = 500;

[UnitX,UnitY,UnitZ] = sphere (NumPoints);

RealX = r * UnitX;
RealY = r * UnitY;
RealZ = r * UnitZ;

x = RealX(:);
y = RealY(:);
z = RealZ(:);

Mask =  2.*y .* (sqrt(r.^2-x.^2-y.^2)./(r.^2)).* sind(15) ...
	+ ((r.^2-2*x.^2-2*y.^2)./(r.^2)) .* cosd(15) ...
	>= cosd(5.8);

% ----------------
figure ('Position', [62,182,1172,338]);

MaskPatchPositive = all ([Mask,z>0], 2);
MaskPatchNegative = all ([Mask,z<0], 2);

% ----------------
subplot (1,3, 1);

hold on
surf (RealX,RealY,RealZ, ...
	'EdgeAlpha', 0.05, ...
	'FaceAlpha', 0.05);
scatter3 (x(Mask),y(Mask),z(Mask),9, ...
	'MarkerEdgeColor', 'none', ...
	'MarkerFaceColor', 'r');
hold off

view ([-35,45]);
grid ('on');
box ('on');
daspect ('auto');
ax = gca;
ax.BoxStyle = 'full';
title ('All points');

% ----------------
subplot (1,3, 2);

hold on
surf (RealX,RealY,RealZ, ...
	'EdgeAlpha', 0.1, ...
	'FaceAlpha', 0.1);
scatter3 (x(MaskPatchPositive),y(MaskPatchPositive),z(MaskPatchPositive),9, ...
	'MarkerEdgeColor', 'none', ...
	'MarkerFaceColor', 'r');
hold off

xlim ([-5,5]);
ylim ([0,15]);
zlim ([45,50]);
grid ('on');
box ('on');
daspect ([1,1,1]);
view ([-60,30]);
ax = gca;
ax.BoxStyle = 'full';
title ('Upper part');

% ----------------
subplot (1,3, 3);

hold on
surf (RealX,RealY,RealZ, ...
	'EdgeAlpha', 0.1, ...
	'FaceAlpha', 0.1);
scatter3 (x(MaskPatchNegative),y(MaskPatchNegative),z(MaskPatchNegative),9, ...
	'MarkerEdgeColor', 'none', ...
	'MarkerFaceColor', 'r');
hold off

xlim ([-5,5]);
ylim ([0,15]);
zlim ([-50,-45]);
grid ('on');
box ('on');
daspect ([1,1,1]);
view ([-60,30]);
ax = gca;
ax.BoxStyle = 'full';
title ('Lower part');

[Alex Lee]

Thanks a lot for your help!

The condition should be the following:

Mask = abs ( ...

2.*y .* (sqrt(r.^2-x.^2-y.^2)./(r.^2)).* sind(15) ...

+ ((r.^2-2*x.^2-2*y.^2)./(r.^2)) .* cosd(15) ...

- cosd(5.8)) >= Epsilon;

But after I changed the condition, the results look a bit wired. Do I need some more adjustment in your program?

Best regards

[Abdolkarim Mohammadi]

You are right. I read the post again and realized that I wrote the condition for = cos(5.8) mistakenly, instead of >= cos(5.8). I revised the code and plots and there is no need for Epsilon anymore. You can increase NumPoints to get better accuracy. If the new code is correct, please mark it as the accepted answer. Thanks.

[Alex Lee]

A lot of thanks!!!